Modulation techniques based on QPSK are commonly used in cellular, personal communication service (PCS) and other types of wireless communication systems. For example, QPSK and offset QPSK (OQPSK) are used in digital wireless systems configured in accordance with the IS-95 standard as described in TIA/EIA/IS-95, "Mobile Station - Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System," June 1996. Other wireless system standards, including IS-54, IS-136 and GSM, also make use of QPSK or a variant thereof. FIG. 1A shows a conventional QPSK modulator 10. An in-phase (I) signal x[n] is passed through a pulse-shaping filter 12, and the output of filter 12 is modulated onto a cosine carrier signal cos(.omega..sub.c t) in mixer 14. A quadrature-phase (Q) signal y[n] is passed through a pulse-shaping filter 16, and the output of filter 16 is modulated onto a sine carrier signal sin(.omega..sub.c t) in mixer 18. The I and Q radio frequency (RF) signals from mixers 14 and 18 are supplied as inputs to a signal combiner 20. The signal combiner 20 combines the I and Q RF signals to form an output QPSK signal z(t) which may be transmitted over a communication channel to a receiver. QPSK modulation thus involves transmitting independent signals on the I and Q components of the signal z(t).
Single sideband (SSB) modulation is a modulation technique that has historically received considerably more attention for analog rather than digital transmission applications, and is described in greater detail in, for example, W. E. Sabin and E. O. Schoenike (Eds.) "Single Sideband Systems & Circuits," 2nd Edition, McGraw-Hill, New York, 1995. FIG. 1B shows a conventional discrete-time SSB modulator 30. An in-phase signal x[n] is passed through a delay element 32 and a pulse-shaping filter 34, and the output of filter 34 is modulated onto cos(.omega..sub.c t) in mixer 36. Unlike QPSK modulation, which as described above transmits independent signals x[n] and y[n] in its respective I and Q components, SSB modulation transmits x[n] in the I component and the Hilbert transform of x[n] in the Q component. The Q component in SSB modulator 30 is therefore generated by passing x[n] through a Hilbert filter 38 and a pulse-shaping filter 40, and modulating the output of filter 40 onto sin(.omega..sub.c t) in mixer 42. A signal combiner 44 combines the I and Q RF signals from mixers 36 and 42 to generate an SSB signal w(t) for transmission. While SSB modulation transmits half the number of bits as QPSK modulation, it also utilizes half the bandwidth, such that SSB and QPSK modulation have the same spectral efficiency.
A conventional QPSK signal generally cannot be transmitted as an SSB signal. For example, the QPSK signal z(t) generated by QPSK modulator 10 may be expressed as: EQU z(t)={x[n]*g(t)}cos(w.sub.c t)+{y[n]*g(t)}sin(w.sub.c t). (1)
Given that x[n], y[n].epsilon.{.+-.1} for QPSK signaling, the transmitted signal z(t) can be written as: ##EQU1## The complex baseband-equivalent representation of the transmitted QPSK signal z(t) may be defined as: EQU z.sub.n =x.sub.n +jy.sub.n. (3)
Similarly, the complex baseband-equivalent representation of the SSB signal w(t) can be written as: EQU w.sub.n =x.sub.n +jx.sub.n. (4)
where x(t)=H {x(t)} and H is the Hilbert transform operator. If the conventional QPSK signal as defined in (3) is transformed into an SSB signal, the resulting signal is given by: EQU (x-y)+j(x+y). (5)
It can be seen from (5) that a conventional SSB transformation of a QPSK signal results in a catastrophic interference between the I and Q components that cannot be removed at the receiver. As a result, SSB transmission is generally not utilized in QPSK communication systems. Similar problems have prevented the use of SSB transmission with other types of similar modulation techniques, including quadrature-amplitude modulation (QAM).